No abstract

On a compact complex manifold X, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if X satisfies the ∂∂-Lemma.

We classify nilmanifolds with an invariant symplectic half-flat structure. We study the transverse or quotient geometry of six-manifolds with an SU(3)-structure preserved by a Killing vector field, giving characterizations in the symplectic half-flat and integrable case.

We study a special type of almost complex structures, called pure and full and introduced by T.J. W. Zhang (arXiv:0708.2520, 2007), in relation to symplectic structures and Hard Lefschetz condition. We provide sufficient conditions to the existence of the above type of almost complex structures on compact quotients of Lie groups by discrete subgroups. We obtain families of pure and full almost complex structures on compact nilmanifolds and solvmanifolds. Some of these families are parametrized by real 2-forms which are anti-invariant with respect to the almost complex structures.

Abstract. We study Bott-Chern cohomology on compact complex non-Kähler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class VII and for compact complex surfaces diffeomorphic to solvmanifolds.